Question

Estimate Values of Expressions with Pi Practice

Answer 1

Sure! Here are some practice problems that involve estimating values of expressions with pi (π). I will provide the questions first and then give you the answers at the end.

### Practice Problems

1. Estimate the circumference of a circle with a radius of 5 units. Use π ≈ 3.14.

2. Calculate the area of a circle with a diameter of 10 units. Use π ≈ 3.14.

3. Find the volume of a cylinder with a radius of 3 units and a height of 7 units. Use π ≈ 3.14.

4. Determine the length of an arc that subtends an angle of 60 degrees in a circle of radius 4 units. Use π ≈ 3.14.

5. Estimate the surface area of a sphere with a radius of 6 units. Use π ≈ 3.14.

### Answers

1. **Circumference**:
\( C = 2\pi r = 2 \cdot 3.14 \cdot 5 \approx 31.4 \) units

2. **Area**:
\( A = \pi r^2 = \pi \left(\frac{10}{2}\right)^2 = \pi \cdot 25 \approx 78.5 \) square units

3. **Volume**:
\( V = \pi r^2 h = \pi \cdot 3^2 \cdot 7 = \pi \cdot 9 \cdot 7 \approx 197.82 \) cubic units

4. **Length of Arc**:
\( L = \frac{\theta}{360} \cdot 2\pi r = \frac{60}{360} \cdot 2 \cdot 3.14 \cdot 4 = \frac{1}{6} \cdot 25.12 \approx 4.19 \) units

5. **Surface Area**:
\( SA = 4\pi r^2 = 4 \cdot \pi \cdot 6^2 = 4 \cdot \pi \cdot 36 \approx 452.16 \) square units

Feel free to try solving these problems on your own before checking the answers!